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Straightening messy correlations with a quantum comb
November 24, 2009
Teasing out unwanted knots in quantum communication, while keeping the information intact Quantum computing promises ultra-fast communication, computation and more powerful ways to encrypt sensitive information. But trying to use quantum states as carriers of information is an extremely delicate business. Now two physicists have shown, mathematically, how to gently tease out unwanted knots in quantum communication, while keeping the information intact. Their work is reported in the current issue of Physical Review Letters and highlighted with a Viewpoint in Physics ( http://physics.aps.org/). When two particles are entangled, they effectively act as a single entity, even though they might be on opposite ends of the galaxy. Physicists can code information into particles to make quantum bits, or qubits, then entangle the qubits in an orderly fashion to form an entangled bit, or ebit. Ebits can then be used to create incredibly tough codes or teleport information between two distant systems. But messy entanglements among particles make qubits more susceptible to losing their encoded information.
Now Dong Yang and Jens Eisert of the University of Potsdam have shown how to delicately comb out a snarl of entanglements among many qubits while keeping the information intact. They designate one qubit as a hub and then use a combination of two existing quantum protocols to transform the original cat's cradle into an arrangement where entanglement fans out neatly from the hub qubit to each of the other qubits. This looks like a primitive model for a quantum World Wide Web: individual users each form an ebit with a single quantum search engine, and send queries and receive results via quantum teleportation.
American Physical Society
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An Introduction to Quantum Computing
by Phillip Kaye (Author), Raymond Laflamme (Author), Michele Mosca (Author)
This concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning graduate students in these disciplines, the text is technically detailed and is clearly illustrated throughout with diagrams and exercises. Some prior knowledge of linear algebra is assumed, including vector spaces and inner products. However, prior familiarity with topics such as tensor products and spectral decomposition is not required, as the necessary material is reviewed in the text.
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Quantum Computing for Computer Scientists
by Noson S. Yanofsky (Author), Mirco A. Mannucci (Author)
The multidisciplinary field of quantum computing strives to exploit some of the uncanny aspects of quantum mechanics to expand our computational horizons. Quantum Computing for Computer Scientists takes readers on a tour of this fascinating area of cutting-edge research. Written in an accessible yet rigorous fashion, this book employs ideas and techniques familiar to every student of computer science. The reader is not expected to have any advanced mathematics or physics background. After presenting the necessary prerequisites, the material is organized to look at different aspects of quantum computing from the specific standpoint of computer science. There are chapters on computer architecture, algorithms, programming languages, theoretical computer science, cryptography, information...
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Quantum Computing: From Linear Algebra to Physical Realizations
by Mikio Nakahara (Author), Tetsuo Ohmi (Author)
Covering both theory and progressive experiments, Quantum Computing: From Linear Algebra to Physical Realizations explains how and why superposition and entanglement provide the enormous computational power in quantum computing. This self-contained, classroom-tested book is divided into two sections, with the first devoted to the theoretical aspects of quantum computing and the second focused on several candidates of a working quantum computer, evaluating them according to the DiVincenzo criteria. Topics in Part I Linear algebra Principles of quantum mechanics Qubit and the first application of quantum information processing—quantum key distribution Quantum gates Simple yet elucidating examples of quantum algorithms Quantum circuits that implement integral transforms ...
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Quantum Computation and Quantum Information
by Michael A. Nielsen (Author), Isaac L. Chuang (Author)
In this first comprehensive introduction to the main ideas and techniques of quantum computation and information, Michael Nielsen and Isaac Chuang ask the question: What are the ultimate physical limits to computation and communication? They detail such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error correction. A wealth of accompanying figures and exercises illustrate and develop the material in more depth. They describe what a quantum computer is, how it can be used to solve problems faster than familiar "classical" computers, and the real-world implementation of quantum computers. Their book concludes with an explanation of how quantum states can be used to perform remarkable feats of communication, and of how it is possible...
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Quantum Computer Science: An Introduction
by N. David Mermin (Author)
In the 1990's it was realized that quantum physics has some spectacular applications in computer science. This book is a concise introduction to quantum computation, developing the basic elements of this new branch of computational theory without assuming any background in physics. It begins with an introduction to the quantum theory from a computer-science perspective. It illustrates the quantum-computational approach with several elementary examples of quantum speed-up, before moving to the major applications: Shor's factoring algorithm, Grover's search algorithm, and quantum error correction. The book is intended primarily for computer scientists who know nothing about quantum theory, but will also be of interest to physicists who want to learn the theory of quantum computation, and...
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Quantum Computing (Natural Computing Series)
by Mika Hirvensalo (Author)
This book is devoted to quantum computing, a new, multidisciplinary research area crossing quantum mechanics, theoretical computer science and mathematics. It contains an introduction to quantum computing as well as the most important recent results on the topic. Two famous algorithms, fast factorization and Grover search, are presented in separate chapters because these inventions are important structurally and developmentally. The presentation of the topic is uniform and computer science-oriented. Thus, the book differs from most of the previous ones which are mainly physics-oriented. The special style of presentation makes the theory of quantum computing accessible to a larger audience, including also the mathematics-oriented oriented readers. Many examples and...
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Quantum Computing Explained
by David McMahon (Author)
A self-contained treatment of the fundamentals of quantum computing This clear, practical book takes quantum computing out of the realm of theoretical physics and teaches the fundamentals of the field to students and professionals who have not had training in quantum computing or quantum information theory, including computer scientists, programmers, electrical engineers, mathematicians, physics students, and chemists. The author cuts through the conventions of typical jargon-laden physics books and instead presents the material through his unique "how-to" approach and friendly, conversational style. Readers will learn how to carry out calculations with explicit details and will gain a fundamental grasp of: * Quantum mechanics ...
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Quantum Computing without Magic: Devices (Scientific and Engineering Computation)
by Zdzislaw Meglicki (Author)
This text offers an introduction to quantum computing, with a special emphasis on basic quantum physics, experiment, and quantum devices. Unlike many other texts, which tend to emphasize algorithms, Quantum Computing without Magic explains the requisite quantum physics in some depth, and then explains the devices themselves. It is a book for readers who, having already encountered quantum algorithms, may ask, "Yes, I can see how the algebra does the trick, but how can we actually do it?" By explaining the details in the context of the topics covered, this book strips the subject of the "magic" with which it is so often cloaked. Quantum Computing without Magic covers the essential probability calculus; the qubit, its physics, manipulation and measurement, and how it can be...
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Classical and Quantum Computation (Graduate Studies in Mathematics)
by A. Yu. Kitaev (Author), A. H. Shen (Author), M. N. Vyalyi (Author)
This book is an introduction to a new rapidly developing theory of quantum computing. It begins with the basics of classical theory of computation: Turing machines, Boolean circuits, parallel algorithms, probabilistic computation, NP-complete problems, and the idea of complexity of an algorithm. The second part of the book provides an exposition of quantum computation theory. It starts with the introduction of general quantum formalism (pure states, density matrices, and superoperators), universal gate sets and approximation theorems. Then the authors study various quantum computation algorithms: Grover's algorithm, Shor's factoring algorithm, and the Abelian hidden subgroup problem. In concluding sections, several related topics are discussed (parallel quantum computation, a quantum...
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Problems And Solutions in Quantum Computing And Quantum Information
by Yorick Hardy Willi-Hans Steeb (Author)
Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. The possibilities of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. This book supplies a collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as to research workers in these fields. All the important concepts and topics such as quantum gates and quantum circuits, entanglement, teleportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error correction, coherent states, squeezed...
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